Characterising the sensor response curve

There are three parameters that contribute to the signal: the gain on the amplifier, the exposure or shutter time and the actual flux of light. In this section I’ll explore these parameters with the goal of achieving a stable signal that responds linearly to changes in light conditions.

Light and exposure time:

The first thing to do is to find saturating conditions that allow for subsequent fine tuning. The first experiment consisted on measuring light at increasing exposure times with 10 ms increments, from 10 to 970 ms. This was done with full light intensity and a gain of 1 (default). From visual inspection already it can be seen that between 40 ms and 50 ms the image starts to show burned pixels, thus to saturate.

40ms.

50 ms.

970 ms.

This is confirmed when the spectra are ploted according to the exposure time:

files = paste0("Data/SingalVsTime Long/",list.files("Data/SingalVsTime Long/"))[c(-1,-99)]
expTimes = files %>% str_extract(pattern = regex("[:digit:]+"))
spectra = map(files,py$get_spectrum) %>% bind_cols()
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spectra = t(spectra) %>% as_tibble()
## Warning: The `x` argument of `as_tibble.matrix()` must have unique column names if `.name_repair` is omitted as of tibble 2.0.0.
## Using compatibility `.name_repair`.
colnames(spectra) = 1:512
spectra$expTimes = expTimes
gathered = spectra %>% gather("pixel","signal",1:512)
gathered$expTimes = gathered$expTimes %>% as.numeric()
gathered$pixel = gathered$pixel %>% as.numeric()
ggplot(gathered,aes(pixel,signal)) + geom_line() + transition_states(expTimes) + labs(title = "Exposure time: {closest_state} us")

Now that the saturating conditions were found, the response of the signal to variations in the exposure time can be explored. This was done by measuring the signal at a fixed gain of 1 and full light intensity at 1 ms intervals from 1 to 49 ms.

files = paste0("Data/SignalVsTime2/",list.files("Data/SignalVsTime2/"))#[-1]
expTimes = files %>% str_extract(pattern = regex("[:digit:]+(?=.d)")) %>% as.numeric()
spectra = map(files,py$get_spectrum) %>% bind_cols()
## New names:
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spectra = t(spectra) %>% as_tibble()
colnames(spectra) = 1:512
spectra$expTimes = expTimes
gathered = spectra %>% gather("pixel","signal",1:512)
gathered$expTimes = gathered$expTimes %>% as.numeric()
gathered$pixel = gathered$pixel %>% as.numeric()
ggplot(gathered,aes(pixel,signal)) + geom_line() + transition_states(expTimes) + labs(title = "Exposure time: {closest_state} us") 

files = paste0("Data/PWM and time/20000/",list.files("Data/PWM and time/20000/"))
percLight = files %>% str_extract(pattern = regex("(?<=_)([:digit:].[:digit:]+)")) %>% as.numeric()
spectra = map(files,py$get_spectrum) %>% bind_cols()
## New names:
## • `` -> `...1`
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spectra = t(spectra) %>% as_tibble()
colnames(spectra) = 1:512
spectra$percLight = percLight
gathered = spectra %>% gather("pixel","signal",1:512)
gathered$pixel = gathered$pixel %>% as.numeric()
ggplot(gathered,aes(pixel,signal)) + geom_line() + transition_states(percLight*100) + labs(title = "Exposure time: {closest_state} %") 

ggplot(gathered, aes(pixel,signal,colour = percLight %>% as.factor())) + geom_line()

files = paste0("Data/PWM and time/40000/",list.files("Data/PWM and time/40000/"))
percLight = files %>% str_extract(pattern = regex("(?<=_)([:digit:].[:digit:]+)")) %>% as.numeric()
spectra = map(files,py$get_spectrum) %>% bind_cols()
## New names:
## • `` -> `...1`
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spectra = t(spectra) %>% as_tibble()
colnames(spectra) = 1:512
spectra$percLight = percLight
gathered = spectra %>% gather("pixel","signal",1:512)
gathered$pixel = gathered$pixel %>% as.numeric()
ggplot(gathered, aes(pixel %>% as.numeric(),signal,colour = percLight %>% as.factor())) + geom_line()

files = paste0("Data/SignalVsTimeVsGain/",list.files("Data/SignalVsTimeVsGain/"))
Gains = files %>% str_extract(pattern = regex("[:digit:]")) %>% as.numeric()
expTimes = files %>% str_extract(pattern = regex("[:digit:]+(?=.d)")) %>% as.numeric()
spectra = map(files,py$get_spectrum) %>% bind_cols()
## New names:
## • `` -> `...1`
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spectra = t(spectra) %>% as_tibble()
colnames(spectra) = 1:512
spectra$expTimes = expTimes
spectra$gains = Gains
spectra = spectra[spectra$expTimes != 0,]
gathered = spectra %>% gather("pixel","signal",1:512)
gathered$expTimes = gathered$expTimes %>% as.numeric()
gathered$pixel = gathered$pixel %>% as.numeric()
gathered$gains = gathered$gains %>% as.factor()
ggplot(gathered,aes(pixel,signal)) + geom_line() + facet_wrap(~gains) + transition_states(expTimes) + labs(title = "Exposure time: {closest_state} us") 

ggplot(gathered[gathered$pixel == 200,],aes(expTimes,signal)) + geom_line() + facet_wrap(~gains)

files = paste0("Data/rep/",list.files("Data/rep/"))#[-1]
expTimes = files %>% str_extract(pattern = regex("[:digit:]+(?=.d)")) %>% as.numeric()
spectra = map(files,py$get_spectrum) %>% bind_cols()
## New names:
## • `` -> `...1`
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spectra = t(spectra) %>% as_tibble()
colnames(spectra) = 1:512
spectra$expTimes = expTimes
gathered = spectra %>% gather("pixel","signal",1:512)
gathered$expTimes = gathered$expTimes %>% as.numeric()
gathered$pixel = gathered$pixel %>% as.numeric()
ggplot(gathered,aes(pixel,signal)) + geom_line() + transition_states(expTimes) + labs(title = "Exposure time: {closest_state} us") 

(apply(spectra, 2, sd)/colMeans(spectra) )%>% .[1:512] %>% plot()

library(rjson)

Results = jsonlite::read_json("Data/results.json")
Spectra = Results %>% map(function(x){x[["spectrum"]]})
Tags = Results %>% map(function(x){x[["tag"]]})
Results[[1]][["spectrum"]]
## [[1]]
## [1] 3.779556
## 
## [[2]]
## [1] 3.652889
## 
## [[3]]
## [1] 2.144
## 
## [[4]]
## [1] 3.101778
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## [[5]]
## [1] 2.289333
## 
## [[6]]
## [1] 2.428
## 
## [[7]]
## [1] 4.011556
## 
## [[8]]
## [1] 3.876
## 
## [[9]]
## [1] 2.946222
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## [[10]]
## [1] 4.448444
## 
## [[11]]
## [1] 2.780889
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## [1] 2.538667
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## [1] 5.029778
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## [1] 4.083556
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## [[15]]
## [1] 3.008
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## [1] 3.411111
## 
## [[17]]
## [1] 3.448
## 
## [[18]]
## [1] 3.327556
## 
## [[19]]
## [1] 3.588444
## 
## [[20]]
## [1] 4.388444
## 
## [[21]]
## [1] 5.192889
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## [[22]]
## [1] 2.150222
## 
## [[23]]
## [1] 4.414667
## 
## [[24]]
## [1] 5.249333
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## [[25]]
## [1] 4.642222
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## [1] 4.910222
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## [[27]]
## [1] 4.735111
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## [1] 3.451556
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## [1] 4.879556
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## [1] 4.297778
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## [1] 4.775556
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## [1] 3.443556
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## [1] 4.874667
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## [1] 4.043556
## 
## [[35]]
## [1] 4.321778
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## [1] 3.921778
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## [1] 5.722667
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## [1] 6.711111
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## [1] 3.853778
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## [1] 4.217333
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## [1] 5.319111
## 
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## [1] 3.832889
## 
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## [1] 5.451556
## 
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## [1] 6.640444
## 
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## [1] 7.134222
## 
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## [1] 6.514222
## 
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## [1] 5.905333
## 
## [[48]]
## [1] 6.337333
## 
## [[49]]
## [1] 8.891111
## 
## [[50]]
## [1] 6.398222
## 
## [[51]]
## [1] 5.652889
## 
## [[52]]
## [1] 4.756
## 
## [[53]]
## [1] 7.154667
## 
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## [1] 9.292
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## [1] 6.461778
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## [1] 6.205778
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## [1] 8.604444
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## [1] 9.536
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## [1] 6.928889
## 
## [[60]]
## [1] 8.984
## 
## [[61]]
## [1] 9.592
## 
## [[62]]
## [1] 7.057778
## 
## [[63]]
## [1] 7.102667
## 
## [[64]]
## [1] 8.797333
## 
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## [1] 10.79067
## 
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## [1] 9.377778
## 
## [[67]]
## [1] 9.034667
## 
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## [1] 9.888444
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## [1] 9.393778
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## [1] 8.493333
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## [1] 11.50844
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## [1] 7.865778
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## [1] 11.28133
## 
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## [1] 10.74178
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## [1] 11.72667
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## [1] 13.06844
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## [1] 15.87022
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## [1] 20.09289
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## [1] 15.76222
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## [1] 20.24622
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## [1] 23.676
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## [1] 34.02933
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## [1] 31.076
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## [1] 34.524
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## [1] 41.00311
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## [1] 32.26756
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## [1] 34.32622
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## [1] 32.74933
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## [1] 31.22044
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## [1] 33.78489
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## [1] 36.52044
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## [1] 32.28178
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## [1] 34.52133
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## [1] 30.75911
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## [1] 39.016
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## [1] 34.508
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## [1] 35.68222
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## [1] 43.20222
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## [1] 55.68889
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## [1] 63.50622
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## [1] 50.948
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## [1] 44.28311
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## [1] 47.01556
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## [1] 51.91022
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Spectra = Spectra %>% map(function(x){x %>% unlist %>% return()}) %>% unlist() %>% matrix(byrow = TRUE,ncol = 512) %>% as_tibble()
colnames(Spectra) = 1:512
Spectra$Tag = Tags %>% map(function(x){x %>% unlist %>% return()}) %>% unlist()
Spectra = separate(Spectra,Tag,into = c("camera","light","percent"),sep = "-")
GatheredSpectra = gather(Spectra,"pixel","Value",1:512)

GatheredSpectra$pixel = as.numeric(GatheredSpectra$pixel)
GatheredSpectra$percent = as.numeric(GatheredSpectra$percent)
GatheredSpectra$camera = as.factor(GatheredSpectra$camera)
GatheredSpectra$light = as.factor(GatheredSpectra$light)
#filter(GatheredSpectra,camera == 1) %>% ggplot(aes(pixel,Value,colour = light)) + geom_line() #+ facet_wrap(~light)

GatheredSpectra %>% ggplot(aes(pixel,Value,colour = percent %>% as.factor())) + geom_line() + facet_grid(rows = vars(light),cols = vars(camera))

#PercMean = Spectra %>% group_by(percent) %>% select(-camera,-light) %>%  summarise_all(mean)
#gather(PercMean,pixel,value,2:513) %>% ggplot(aes(pixel %>% as.numeric(),value %>% as.numeric(),colour = as.factor(percent))) + geom_line()

filter(GatheredSpectra,camera == 1,light == 1,pixel == 300) %>% ggplot(aes(Value,percent)) + geom_line() 

nestedSpectra = Spectra %>% group_by(light,camera) %>% nest()
library(pls)
PLSR = function(x){
  model = pls::plsr(percent ~ ., data = x, ncomp = 1, validation = "LOO")
  return(model)
}
models = nestedSpectra$data %>% map(PLSR)
par(mfrow= c(2,5))
for(i in 1:10){
  plot(models[[i]])
}

par(mfrow= c(1,1))